Description: If a set of reals contains a lower bound, the lower bound is its infimum. (Contributed by NM, 9-Oct-2005) (Revised by AV, 4-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | lbinf | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltso | |
|
2 | 1 | a1i | |
3 | lbcl | |
|
4 | ssel | |
|
5 | 4 | adantr | |
6 | 3 5 | mpd | |
7 | 6 | adantr | |
8 | ssel2 | |
|
9 | 8 | adantlr | |
10 | lble | |
|
11 | 10 | 3expa | |
12 | 7 9 11 | lensymd | |
13 | 2 6 3 12 | infmin | |